In a medium bowl, whisk together the flour, baking soda and salt. Using an electric mixer, beat the sugar and butter on high speed until light and fluffy, about 2 minutes. Beat in the egg and vanilla, scraping the bowl as necessary. Gradually beat in the dry ingredients on low speed.
Shape the dough into 2 balls. Place each ball between 2 sheets of wax paper and roll out to a 10-inch round. Slide onto a cookie sheet and refrigerate until chilled, about 1 hour.
Preheat the oven to 350 degrees . Using a 2 1/2-inch animal-shape cookie cutter, cut the dough into cookies, gathering scraps and re-rolling until all the dough has been cut. Place cookies 1 inch apart on parchment-paper-lined cookie sheets. Bake until the edges are golden-brown, 15-20 minutes. Let cool.
In a small saucepan, melt the white chocolate over low heat, stirring, until glossy. Using a small offset spatula, spread the chocolate on the cookies and transfer to a wax-paper-lined cookie sheet. Top with the sprinkles. Refrigerate until set, about 1 hour.